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Bulletin of the American Physical Society

Protected qubits and quantum computation using Josephson junctions

Alexei Kitaev

Published Mar 15, 2006• 0 citations
OpenAlex

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We propose a complete quantum computation process on a topologically protected Josephson junction array system, originally proposed by Ioffe and Feigel'man [Phys. Rev. B 66, 224503 (2002)]. Logical qubits for computation are encoded in the punctured array. The number of qubits is determined by the number of holes. The topological degeneracy is lightly shifted by tuning the flux along specific paths. We show how to perform both single-qubit and basic quantum-gate operations in this system, especially the controlled-NOT (CNOT) gate.
Superconducting protected qubits aim to achieve sufficiently low error rates so as to allow realization of error-corrected, utility-scale quantum computers. A recent proposal encodes a protected qubit in the quasicharge degree of freedom of the conventional transmon device. Operating such a protected `quasicharge qubit' requires implementing new strategies. Here we show that an electronically-controllable tunnel junction formed by two topological superconductors can be used to implement single- and two-qubit gates on quasicharge qubits. Schemes for both these gates are based on the same dynamical 4π4π4π-periodic Josephson effect and therefore have the same gate times and error characteristics. We simulate the dynamics of a topological Josephson junction in a parameter regime with non-negligible charging energy, and characterize the robustness of such gate operations against charge noise. Our results point to a compelling strategy for implementation of quasicharge qubit gates based on junctions of minimal Kitaev chains of quantum dots.